Argument from ignorance (Latin: argumentum ad ignorantiam), also known as appeal to ignorance (in which ignorance stands for "lack of evidence to the contrary"), is a fallacy in informal logic. It asserts that a proposition is true because it has not yet been proven false (or vice versa). This represents a type of false dichotomy in that it excludes a third option, which is that there is insufficient investigation and therefore insufficient information to prove the proposition satisfactorily to be either true or false. Nor does it allow the admission that the choices may in fact not be two (true or false), but may be as many as four,

Arguments that appeal to ignorance rely merely on the fact that the veracity of the proposition is not disproven to arrive at a definite conclusion. These arguments fail to appreciate that the limits of one's understanding or certainty do not change what is true. They do not inform upon reality. That is, whatever the reality is, it does not "wait" upon human logic or analysis to be formulated. Reality exists at all times, and it exists independently of what is in the mind of anyone[citation needed]. And the true thrust of science and rational analysis is to separate preconceived notion(s) of what reality is, and to be open at all times to the observation of nature as it behaves, so as truly to discover reality. This fallacy can be very convincing and is considered by some[2] to be a special case of a false dilemma or false dichotomy in that they both fail to consider alternatives. A false dilemma may take the form:

If a proposition has not been disproven, then it cannot be considered false and must therefore be considered true.

If a proposition has not been proven, then it cannot be considered true and must therefore be considered false.

Such arguments attempt to exploit the facts that (a) true things can never be disproven and (b) false things can never be proven. In other words, appeals to ignorance claim that the converse of these facts are also true. Therein lies the fallacy.

To reiterate, these arguments ignore the fact, and difficulty, that some true things may never be proven, and some false things may never be disproved with absolute certainty. The phrase "the absence of evidence is not the evidence of absence" can be used as a shorthand rebuttal to the second form of the ignorance fallacy (i.e. P has never been absolutely proven and is therefore certainly false). Most often it is directed at any conclusion derived from null results in an experiment or from the non-detection of something. In other words, where one researcher may say their experiment suggests evidence of absence, another researcher might argue that the experiment failed to detect a phenomenon for other reasons.

Much confusion about arguments from ignorance can be caused when one side of a debate forgets that we often possess evidence of absence in practice.

The ignorance fallacy is sometimes confused (or combined) with logically valid contrapositive arguments. Contrapositive arguments rightly utilize the transposition rule of inference in classical logic to conclude something like: To the extent that C implies E then Not-E must also imply Not-C. In other words, if a cause always leads to an effect, then absence of the expected effect is evidence of absence of the cause. For example, if the causal proposition that If it's raining outside then the streets will be wet is assumed, then it can be assumed that if the streets are not wet then it is not raining outside. The inference that it cannot be raining outside because the streets are not getting wet is exactly as true, or perhaps exactly as untrue, as the original proposition. The statements are logically equivalent.

Appeal to ignorance: the claim that whatever has not been proved false must be true, and vice versa. (e.g., There is no compelling evidence that UFOs are not visiting the Earth; therefore, UFOs exist, and there is intelligent life elsewhere in the Universe. Or: There may be seventy kazillion other worlds, but not one is known to have the moral advancement of the Earth, so we're still central to the Universe.) This impatience with ambiguity can be criticized in the phrase: absence of evidence is not evidence of absence.[3]

For instance, absence of evidence that it rained (i.e. water is the evidence) may be considered positive evidence that it did not rain. Again, in science, such inferences are always made to some limited (sometimes extremely high) degree of probability and in this case absence of evidence is evidence of absence when the positive evidence should have been there but is not.

Arguments from ignorance can easily find their way into debates over the existence of God. It is a fallacy to draw conclusions based precisely on ignorance, since this does not satisfactorily address issues of philosophic burden of proof. But null results are not ignorance and can be used as evidence to achieve a given burden of proof.

Contraposition is a logically valid rule of inference that allows the creation of a new proposition from the negation and reordering of an existing one. The method applies to any proposition of the type If A then B and says that negating all the variables and switching them back to front leads to a new proposition i.e. If Not-B then Not-A that is just as true as the original one and that the first implies the second and the second implies the first.

Transposition is exactly the same thing described in a different language.

Evidence of absence is evidence of any kind that can be used to infer or deduce the non-existence or non-presence of something. For instance, if a doctor does not find any malignant cells in a patient this null result (finding nothing) is evidence of absence of cancer, even though the doctor has not actually detected anything per se. Such inductive reasoning is important to empiricism and science, but has well established limitations. The challenge thus becomes to try to identify when a researcher has received a null result (found nothing) because the thing does not exist (evidence of absence - objectively negative result), and when one simply lacks proper means of detection (absence of evidence - false negative).

Negative evidence is sometimes used as an alternative to absence of evidence and is often meant to be synonymous with it. On the other hand, the term may also refer to evidence with a negative value, or null result equivalent to evidence of absence. It may even refer to positive evidence about something of an unpleasant nature.

Null result is a term often used in the field of science to indicate evidence of absence. A search for water on the ground may yield a null result (the ground is dry); therefore, it probably did not rain.

P is too incredible (or: I cannot imagine how P could possibly be true); therefore P must be false.

I cannot imagine how P could possibly be false; therefore P must be true.

These arguments are similar to arguments from ignorance in that they too ignore and do not properly eliminate the possibility that something can be both incredible and still be true, or appear to be obvious and yet still be false.

If P were true then I would know it; in fact I do not know it; therefore P cannot be true.

If P were false then I would know it; in fact I do not know it; therefore P cannot be false.

In practice these arguments are often fallacious and rely on the veracity of the supporting premise. For example the argument that If I had just sat on a wild porcupine then I would know it; in fact I do not know it; therefore I did not just sit on a wild porcupine is probably not a fallacy and depends entirely on the veracity of the leading proposition that supports it. (See Contraposition and Transposition in the Related terms section in this article.)

Absence of evidence is a condition in which no valid conclusion can be inferred from the mere absence of detection, normally due to doubt in the detection method. Evidence of absence is the successful variation: a conclusion that relies on specific knowledge in conjunction with negative detection to deduce the absence of something. An example of evidence of absence is checking your pockets for spare change and finding nothing, but being confident that the search would have found it if it was there.

By determining that a given experiment or method of detection is sensitive and reliable enough to detect the presence of X (when X is present) one can confidently exclude the possibility that X may be both undetected and present. This allows one to deduce that X cannot be present if a null result is received.

Thus there are only two possibilities, given a null result:

Nothing detected, and X is not present.

Nothing detected, but X is present (option eliminated by careful research design).

To the extent that option 2 can be eliminated, one can deduce that if X is not detected then X is not present and therefore the null result is evidence of absence.

(Draws a conclusion based on lack of knowledge or evidence without accounting for all possibilities)

"I take the view that this lack (of enemy subversive activity in the west coast) is the most ominous sign in our whole situation. It convinces me more than perhaps any other factor that the sabotage we are to get, the Fifth Column activities are to get, are timed just like Pearl Harbor ... I believe we are just being lulled into a false sense of security." – Earl Warren, then California's Attorney General (before a congressional hearing in San Francisco on 21 February 1942)

One looks in the back seat of one's car and finds no adult-sized kangaroos and then uses this negative/null adult-sized kangaroo detection results in conjunction with the previously determined fact (or just plain old proposition) that adult-sized kangaroos, if present, cannot evade such detection, to deduce a new fact that there are indeed no adult-sized kangaroos present in the back seat of said car.

The presumption of innocence, if present, effectively removes the possibility that the accused may be both guilty and unproven, from consideration in judgment, and as such the accused is considered as innocent unless proven guilty. (See decision table below)

From Fallacies: classical and contemporary readings by Hans V. Hansen, Robert C. Pinto:

"It is generally accepted that the philosopher John Locke introduced the term in his Essay Concerning Human Understanding:"

"Another way that Men ordinarily use to drive others, and force them to submit their Judgments. And receive the Opinion in debate, is to require the Adversary to admit what they alledge as a Proof, or assign a better. And this I call Argumentum ad Ignorantiam" — John Locke[4]